The notion of homotopy relative Rota-Baxter operators in the context of \(A_\infty \) -algebras (strongly homotopy associative algebras) was introduced in [1]}. Like the classical case, a homotopy relative Rota-Baxter algebra consists of an \(A_\infty \) -algebra \(\mathcal {A}\) , an \(\mathcal {A}\) -bimodule \(\mathcal {M}\)  and a homotopy relative Rota-Baxter operator. In this paper, we consider homotopy relative Rota-Baxter algebras whose underlying graded vector spaces \(\mathcal {A}, \mathcal {M}\)  are concentrated in degrees 0 and 1. In particular, we classify skeletal homotopy relative Rota-Baxter algebras by third cocycles of relative Rota-Baxter algebras introduced in the present paper (cf. Theorem REF ).
